I am currently a post doctoral scholar, under the mentorship of
Kathrin Bringmann, at the University of Cologne.
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University of Cologne
My research interests are centered around integer partitions by
q-series, modular forms,
harmonic Maass forms, special functions, and combinatorics.
In particular I am interested in
congruences for partition functions that are not modular
forms, introducing new cranks for
partition functions, and studying rank functions
via harmonic Maass forms. Additionally I enjoy
all partition functions and q-series identities
coming from Bailey pairs and Bailey's Lemma.
I am a strong advocate for explicit computations for conjectures and verifications of theorems.
Primarily my computations are done in Maple.
The current version of my CV in pdf format can be found here.
The majority of my articles can be found on
Preprints and Submitted Work
Projects in Progress
Mock modularity of the Md-rank of overpartitions
(with H. Swisher)
submitted for publication
Asymptotics and Inequalities for the M2-partition Rank Function
(with D. Reihill)
When Fourth Moments are Enough
(with D. Skinner and E. Waymire),
to appear in Rocky Mountain Journal of Mathematics (8 pages)
The Generating Function of the M2-rank of Partitions without Repeated Odd Parts as a Mock Modular Form
accepted for publication in Transactions of the American Mathematical Society (28 pages)
On a modularity conjecture of Andrews, Dixit, Schultz, and Yee for a variation of Ramamunjan's ω(q)
(with K. Bringmann and K. Mahlburg)
Advances in Mathematics, Vol. 325, pages 505--532 (2018)
Some Smallest Parts Functions from Variations of Bailey's Lemma
in Frontiers in Orthogonal Polynomials and q-Series, Chapter 18, pages 343-372 (2018)
Ranks For Two Partition Quadruple Functions
Journal de Theorie de Nombres de Bordeaux, Vol. 29 number 2, pages 425-443 (2017)
Two Partition Functions with Congruences modulo 3, 5, 7, and 13
Annals of Combinatorics, Vol. 21 number 3, (2017), pages 397-443
Exotic Bailey-Slater SPT-Functions I: Group A
Advances in Mathematics, Vol. 305, (2017), pages 479-514
Higher Order Smallest Parts Functions and Rank-Crank Moment Inequalities from Bailey Pairs
(with C. Babecki and G. Sangston)
Research in Number Theory, Vol. 2(1), (2016), pages 1-35
Exotic Bailey-Slater SPT-Functions II: Hecke-Rogers-Type Double Sums and
Bailey Pairs From Groups A, C, E
(with F. Garvan)
Advances in Mathematics, Vol. 299, (2016), pages 605-639
Exotic Bailey-Slater SPT-Functions III: Bailey Pairs from Groups B, F, G, and J
Acta Arithmetica, Vol. 173 Number 4, (2016), pages 317-364,
Overpartition Rank Differences Modulo 7 by Maass Forms
Journal of Number Theory, Vol. 163, (2016), pages 331-358,
Congruences for Partition Pairs with Conditions
(formerly titled "Congruences for a Certain Partition Pair by a Crank"),
Quarterly Journal of Mathematics, Vol. 66, No. 3 (2015), pages 837-860
Rank and Crank Moments for Partitions without Repeated Odd Parts,
Int. J. Number Theory, Vol. 11, No. 03 (2015), pages 683-703.
Higher Order SPT functions for overpartitions, overpartitions with smallest part even,
and partitions without repeated odd parts
Journal of Number Theory, Vol. 149, (2015), pages 285-312.
Another SPT crank for the number of smallest parts in overpartitions with even smallest part
(formerly titled "Another proof of two modulo 3 congruences and another SPT crank for the number of
smallest parts in overpartitions with even smallest part"),
Journal of Number Theory, Vol. 148, (2015), pages 196-203.
The spt-crank for overpartitions
(with F. Garvan),
Acta Arithmetica, Vol. 166, No. 02 (2014), pages 141-188.
Hecke-type congruences for Andrews' spt-function modulo 16 and 32
(with F. Garvan),
Int. J. Number Theory, Vol. 10, No. 02 (2014), pages 375-390.
A note on the transcendence of zeros of a certain family of weakly holomorphic modular forms
(with H. Swisher),
Int. J. Number Theory, Vol. 10, No. 02 (2014), pages 309-317.